Fig. 1 - "Pogo" affects a rocket by causing it to
bounce up and down along its direction of flight like a pogo
stick. (NASA: KSC-69PC-413, annotated)

"Pogo" is a rocket scientist's slang for a longitudinal vibration or
oscillation that sometimes occurs in rockets. As the propellant flows
through the pipes and fittings on its way from the tanks to the
engine, low-frequency disturbances can form. This disturbance is like
the groaning of plumbing pipes in your house, only not as strong.
Since this causes variations in the propellant flow rate, the thrust
from the affected engines fluctuates several times a second.

Periodic fluctuations in thrust occur in all rocket engines, but
normally the mass of the rocket is sufficient to keep it from becoming
noticeable or dangerous. But when the thrust fluctuation approaches
the resonant frequency of the rocket structure, the forces "couple"
and the result is the sense that the rocket is surging backward and
forward along its length several times a second. This motion
resembles that of a pogo stick, hence the name.[Sutton01, p. 350]

The curious feature of pogo is its ability to feed back on itself.
The thrust fluctuation caused by unsteady propellant rates in turn
causes more unsteadiness in the propellant. Imagine you're in your
car, just pulling away from a stop. Now you pull the seat release to
allow it to move forward or backward. (Disclaimer: don't actually do
this; it's dangerous.) Since the car is accelerating, you slide
backward. But this removes your foot from the accelerator, and so the
car begins to slow. As it does, you slide forward and your foot
re-engages the accelerator, causing you to speed up and the seat to
slide backward, and so forth.

Engineers eliminate pogo either by adjusting the frequencies at
which the structure or propellants vibrate, or by "damping" the
vibration in either or both. You can, for example, change the lengths
of propellant pipe segments, or put "shock absorbers" in them.

Continuing combustion
instability problems in the F-1 engine caused pogo effects in the
Saturn V all the way up to Apollo 10, after which everything worked
perfectly. [Mary Bennet and David Percy, Dark Moon,
p. 128]

There are many things wrong with this statement. First, the
combustion instability of the F-1 observed during its development was
not the cause of the pogo. Pogo in turn introduces a different
kind of combustion instability in the engine, but it has nothing to do
with the standing-wave type of instability. Pogo is a structural
dynamics problem. If left alone it will not necessarily damage the
engine, but it may damage the rocket structure and damage the
payload. Standing-wave instability is a fluid dynamics
problem. Left unchecked it will quickly destroy the engine by
creating "hot spots" in the thrust chamber that weaken and fail.

Fig. 2 - A strategy for pogo suppression in propellant
lines. Pogo-induced pressure waves (a) are damped by the
compression of a trapped gas (b), usually helium.

Second, there was no one single mission before which pogo was a
serious problem, and after which it wasn't. Pogo occurred in the
Saturn V all the way up to Apollo 17. But during the program
engineers took a series of steps to make pogo less of a problem for
each successive mission. But there was often a delay because
engineers needed time to analyze the results from a Saturn V flight,
and in most cases the next Saturn V was already "stacked" in the
assembly building and couldn't be easily modified.

Apollo 6 - First use of pogo-damping surge absorbers
(Fig. 2) on the first-stage outboard F-1 engines. (The outboard
engines have roughly similar propellant line geometries while the
center engine's propellant lines are considerably different than the
other four.)

Apollo 10 - Early programmed shutdown of the
second-stage center J-2 engine as pogo became apparent in that
stage. This was first noticed on Apollo 8.

Apollo 14 - First use of pogo-damping surge absorber
installed on the center J-2 engine. A different pogo problem than the
one from Apollo 8 developed in the second stage on Apollos 11 and 12.
On Apollo 13 this center J-2 pogo was the cause of the premature
shutdown (even before the planned shutdown). Good thing too, because
it was later determined that the J-2 thrust structure was vibrating so
badly that it would have collapsed had the Saturn V's computer not
shut it down when it did. The surge absorber for the J-2 had already
been designed and built prior to Apollo 13, but it was too late to
install it in the rocket.

It's pretty clear, looking at the history of pogo effects on the
Saturn V, that the authors are wrong when they suggest that
"everything worked perfectly" after Apollo 10. The authors are trying
to create the impression that the Saturn V "suspiciously" worked
flawlessly after a number of serious problems in its development. But
the facts (most of which the authors don't discuss) suggest a more
gradual and progressive improvement.

The center F-1 engine of
the Saturn V first stage was shut off early in order to fix the pogo
problem. [Ibid.]

The authors' source for this statement is BBC aerospace
correspondent Reginald Turnill. As journalists go, Turnill is quite
competent. But he is still a secondary source, and it's not clear
from Dark Moon whether Turnill or the authors connected the
early F-1 shutoff with pogo suppression.

It's true that the center F-1 engine was shut down early, but this
was not to solve a pogo problem. It was to reduce the rocket's
acceleration just prior to staging. As the Saturn V climbs on its
first stage it consumes a large amount of fuel, thereby reducing its
mass. The air becomes thinner and offers less resistance to both the
escaping exhaust (i.e., thrust increases) and to the rocket itself
(i.e., drag decreases). This combination of factors means the Saturn
V's acceleration near the end of the first-stage burn would be
tremendous if all five of the F-1 engines were allowed to keep firing.
Not only would this stress the crew, it would also provide a
tremendous jolt when the first stage stopped firing.

This would not have reduced the Saturn V's performance
significantly, as the authors fear, because it happened fairly late in
the boost, just a few seconds before the first stage was scheduled to
stop anyway.

Pogo affected the outboard F-1s, not the inboard engine.

Other authors say the
second-stage's center engine was cut off early in order to solve the
pogo problem. But the problem was on the first stage, so how
would this have helped?

Had Dark Moon's authors thoroughly researched the pogo
issue in the Saturn V they would have discovered that pogo occurred
during the operation of both the first and second stages. As it is,
they seem to have confused pogo with the F-1 combustion instability
problems and therefore they have wrongly concluded that pogo was a
first-stage problem only.

The Dark Moon authors attempt to lay blame at NASA's feet
for this apparent discrepancy in accounts. However it is clear that
the discrepancy derives from the authors' inattention to detail and
their confusion of related but different rocketry problems.